The Aussie actor, 46, revealed that he met up with the Indiana Jones star while they were staying at the same hotel.
“My kids are obsessed with Harrison Ford and his films,” Crowe said.
“They love him, they love Indiana Jones and now they are into Star Wars.
“He was in the same hotel as me the other day doing a press junket.”
He added: “I sent him a note and asked if there was any way we could get five minutes together and maybe have a photo together because it would make me look like a genius in front of my kids.
“He was really kind about it and did a shot and signed some autographs for them.”
Referring to the picture, host Letterman quipped: “It looks to me like you have your hand on Harrison’s .”
Crowe fired back: “But its not as if he’s not enjoying it – there’s definitely pleasure in that look!